Higgs inflation in Gauss-Bonnet braneworld

Rong-Gen Cai, Zong-Kuan Guo, and Shao-Jiang Wang

Phys. Rev. D 92, 063514 – Published 11 September 2015

Abstract

The measured masses of the Higgs boson and top quark indicate that the effective potential of the standard model either develops an unstable electroweak vacuum or stands stable all the way up to the Planck scale. In the latter case in which the top quark mass is about $2 σ$ below its present central value, the Higgs boson can be the inflaton with the help of a large nonminimal coupling to curvature in four dimensions. We propose a scenario in which the Higgs boson can be the inflaton in a five-dimensional Gauss-Bonnet braneworld model to solve both the unitarity and stability problems which usually plague Higgs inflation. We find that in order for Higgs inflation to happen successfully in the Gauss-Bonnet regime, the extra dimension scale must appear roughly in the range between the TeV scale and the instability scale of standard model. At the tree level, our model can give rise to a naturally small nonminimal coupling $ξ \sim O (1)$ for the Higgs quartic coupling $λ \sim O (0.1)$ if the extra dimension scale lies at the TeV scale. At the loop level, the inflationary predictions at the tree level are preserved. Our model can be confronted with future experiments and observations from both particle physics and cosmology.

Received 15 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.063514

Authors & Affiliations

Rong-Gen Cai^*, Zong-Kuan Guo^†, and Shao-Jiang Wang^‡

State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

^*cairg@itp.ac.cn
^†guozk@itp.ac.cn
^‡schwang@itp.ac.cn

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Vol. 92, Iss. 6 — 15 September 2015

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Images

Figure 1
The evolution of brane universe with different choices of $β$ . The vertical and horizontal axis describe the inflationary Hubble scale $H^{2} / μ^{2}$ and energy density scale $ρ / μ^{2}$ on the brane, respectively, for a given extra dimension scale $μ$ . With decreasing $β$ from 1 to 0, the GB regime is pushed toward to even higher energy scale and the RS regime grows slowly to finally dominate after its emergence when GB energy scale finally wins over the RS energy scale.
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Figure 2
The characteristic features of Higgs inflation with respect to the energy scale $μ$ of extra dimension in the Gauss-Bonnet braneworld. In the first panel, GR regime with $\frac{H}{μ} ≪ 1$ is found for $μ ≳ 10^{12} GeV$ and GB regime with $\frac{H}{μ} ≫ 1$ is found for $μ ≲ 10^{12} GeV$ . In the second panel, the field values at the start/end point of inflation remain constant in the GR regime but increase significantly in the GB regime. However, the field excursion of inflation is about $5 M_{4}$ for all $μ$ . In the third panel, the inflationary Hubble scales are shown with respect to the extra dimension scale. In the left hand side of purple line where the inflationary Hubble scale equals to the extra dimension scale, the extra dimension scale appears below the inflationary Hubble scale. In the last panel, we summarize several typical energy scales with respect to the extra dimension scale.
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Figure 3
The prediction of combined parameter $\frac{λ}{ξ^{2}}$ for Higgs inflation with respect to the energy scale $μ$ of extra dimension in the Gauss-Bonnet braneworld. For $μ$ larger than $10^{12} GeV$ , $\frac{λ}{ξ^{2}}$ remains constant around $10^{- 10}$ as in the four-dimensional case. For $μ$ smaller than $10^{12} GeV$ , $\frac{λ}{ξ^{2}}$ increases significantly but the product $\frac{μ}{M_{4}} \frac{λ}{ξ^{2}}$ remains constant around $10^{- 16}$ . For $μ$ around TeV scale, $\frac{λ}{ξ^{2}}$ is of order $O (0.1)$ , which can lead to a naturally small $ξ \sim O (1)$ for $λ \sim O (0.1)$ .
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Figure 4
Inflationary predictions for Higgs inflation in the Gauss-Bonnet braneworld. The first three panels show the predictions of scalar spectral index $n_{s}$ , tensor-to-scalar ratio $r$ , and the running of scalar spectral index $α_{s}$ with respect to the energy scale $μ$ of extra dimension. With decreasing $μ$ , $r$ drops significantly while $n_{s}$ and $α_{s}$ remain almost the same as in the four-dimensional case. In the last panel, the inflationary predictions of $n_{s}$ and $r$ are showed in the $n_{s} - r$ plane, where the red points represent the case of four-dimensional Higgs inflation.
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Figure 5
Numerical results of nonminimal coupling $ξ_{\inf}$ , Higgs quartic coupling $λ_{\inf}$ , scalar spectral index $n_{s}$ and tensor-to-scalar ratio $r$ during inflation with respect to the top quark mass assuming the Higgs mass $m_{h} = 125.66 GeV$ . The extra dimension scale is 10 TeV for the blue region and 50 TeV for the red region respectively, where the $1 σ$ uncertainties are mainly from strong coupling $α_{s}$ along with other theoretical uncertainties from the threshold corrections.
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Figure 6
The upper bound of top quark mass $m_{t}$ as a function of Higgs mass $m_{h}$ where we have taken into account the $1 σ$ uncertainties from strong coupling $α_{s}$ along with other theoretical uncertainties from the threshold corrections. As comparisons, we also provide the upper bound set by four-dimensional Higgs inflation and the experimental constraint on $m_{t}$ and $m_{h}$ .
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